is :

Let A be an orthogonal non-singular matrix of order n, then  is equal to :

‘A’ is any square matrix, then det  is equal to :

 represent the sides of a triangleABC, then  is equal to :

    :

If a, b, c are the sides of a ΔABC opposite to angle A, B, C respectively, then

                             :

The value of  lying between  and satisfying the equation  

        :

          .

has a non-zero solution, then value of  

If a determinate of  is formed by using the number 1 or –1 then minimum value of determinant is :

A and B are square matrices and A is non-singular matrix,  : 

The value of  such that the system x – 2y + z = –4, 2x – y + 2z = 2,  has no solution is :